Simplify ((-3x^5m^-3)^5)/(12x^-1m^2)

$\frac{{(- 3 x^{5} m^{- 3})}^{5}}{12 x^{- 1} m^{2}}$

Step 1

Move $x^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(- 3 x^{5} m^{- 3})}^{5} x}{12 m^{2}}$

Step 2

Simplify the numerator.

Apply the product rule to $- 3 x^{5} m^{- 3}$ .

$\frac{{(- 3 x^{5})}^{5} {(m^{- 3})}^{5} x}{12 m^{2}}$

Apply the product rule to $- 3 x^{5}$ .

$\frac{{(- 3)}^{5} {(x^{5})}^{5} {(m^{- 3})}^{5} x}{12 m^{2}}$

Raise $- 3$ to the power of $5$ .

$\frac{- 243 {(x^{5})}^{5} {(m^{- 3})}^{5} x}{12 m^{2}}$

Multiply the exponents in ${(x^{5})}^{5}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- 243 x^{5 \cdot 5} {(m^{- 3})}^{5} x}{12 m^{2}}$

Multiply $5$ by $5$ .

$\frac{- 243 x^{25} {(m^{- 3})}^{5} x}{12 m^{2}}$

Multiply the exponents in ${(m^{- 3})}^{5}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- 243 x^{25} m^{- 3 \cdot 5} x}{12 m^{2}}$

Multiply $- 3$ by $5$ .

$\frac{- 243 x^{25} m^{- 15} x}{12 m^{2}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 243 x^{25} \frac{1}{m^{15}} x}{12 m^{2}}$

Combine exponents.

Combine $- 243$ and $\frac{1}{m^{15}}$ .

$\frac{x^{25} \frac{- 243}{m^{15}} x}{12 m^{2}}$

Combine $x^{25}$ and $\frac{- 243}{m^{15}}$ .

$\frac{\frac{x^{25} \cdot - 243}{m^{15}} x}{12 m^{2}}$

Combine $\frac{x^{25} \cdot - 243}{m^{15}}$ and $x$ .

$\frac{\frac{x^{25} \cdot - 243 x}{m^{15}}}{12 m^{2}}$

Raise $x$ to the power of $1$ .

$\frac{\frac{- 243 (x^{25} x^{1})}{m^{15}}}{12 m^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\frac{- 243 x^{25 + 1}}{m^{15}}}{12 m^{2}}$

Add $25$ and $1$ .

$\frac{\frac{- 243 x^{26}}{m^{15}}}{12 m^{2}}$

Move the negative in front of the fraction.

$\frac{- \frac{243 x^{26}}{m^{15}}}{12 m^{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{243 x^{26}}{m^{15}} \cdot \frac{1}{12 m^{2}}$

Step 4

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{243 x^{26}}{m^{15}}$ into the numerator.

$\frac{- 243 x^{26}}{m^{15}} \cdot \frac{1}{12 m^{2}}$

Factor $3$ out of $- 243 x^{26}$ .

$\frac{3 (- 81 x^{26})}{m^{15}} \cdot \frac{1}{12 m^{2}}$

Factor $3$ out of $12 m^{2}$ .

$\frac{3 (- 81 x^{26})}{m^{15}} \cdot \frac{1}{3 (4 m^{2})}$

Cancel the common factor.

$\frac{3 (- 81 x^{26})}{m^{15}} \cdot \frac{1}{3 (4 m^{2})}$

Rewrite the expression.

$\frac{- 81 x^{26}}{m^{15}} \cdot \frac{1}{4 m^{2}}$

Step 5

Multiply $\frac{- 81 x^{26}}{m^{15}}$ by $\frac{1}{4 m^{2}}$ .

$\frac{- 81 x^{26}}{m^{15} (4 m^{2})}$

Step 6

Multiply $m^{15}$ by $m^{2}$ by adding the exponents.

Move $m^{2}$ .

$\frac{- 81 x^{26}}{m^{2} m^{15} \cdot 4}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 81 x^{26}}{m^{2 + 15} \cdot 4}$

Add $2$ and $15$ .

$\frac{- 81 x^{26}}{m^{17} \cdot 4}$

Step 7

Move $4$ to the left of $m^{17}$ .

$\frac{- 81 x^{26}}{4 \cdot m^{17}}$

Step 8

Move the negative in front of the fraction.

$- \frac{81 x^{26}}{4 m^{17}}$

Simplify ((-3x^5m^-3)^5)/(12x^-1m^2)

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